Question

The present value of a payment of 1004 at the end of T months is equal to the sum of the present values of the following payments (i) 314 at the end of 1 month (ii) 271 at the end of 18 months i) 419 at the end of 24 months For all payments, the effective annual interest rate is 5%. Calculate T. Round your answer to the nearest whole number.

Answer 1

Presnet value of payment 1 = 314/(1+r/12)^(n)

where r is interet rate

and n is number of month

PV of payment 1 = 314/(1+.05/12)^1 = 312.7

PV of payment 2 = 271/(1+.05/12)^18 = 251.46

PV of payment 3 = 419/(1 + .05/12)^24 = 379.2

Sum of all payments = 943.36

now we will equate the both side

1004/(1+.05/12)^T = 943.36

1.004167^T = 1.064281

T = ln(1.064281)/ln(1.004167) = 15 months